{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/princegrover/anaconda3/lib/python3.6/site-packages/statsmodels/compat/pandas.py:56: FutureWarning: The pandas.core.datetools module is deprecated and will be removed in a future version. Please use the pandas.tseries module instead.\n",
      "  from pandas.core import datetools\n"
     ]
    }
   ],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.linear_model import LinearRegression\n",
    "import statsmodels.api as sm\n",
    "import statsmodels.formula.api as smf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [],
   "source": [
    "y = np.arange(1,25, 0.25)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "# linear relationship with contant variance of residual\n",
    "\n",
    "x1 = y.copy() + np.random.randn(96)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 155,
   "metadata": {},
   "outputs": [],
   "source": [
    "# non contant variance with residuals \n",
    "\n",
    "x2 = y.copy()\n",
    "y2 = x2 + np.concatenate((np.random.randn(20)*0.5,\n",
    "                                np.random.randn(20)*1, \n",
    "                                np.random.randn(20)*4, \n",
    "                               np.random.randn(20)*6, \n",
    "                               np.random.randn(16)*8), axis=0) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 156,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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O0esVjMzcJ+nvJb3e3e/t94Xd/UeS3iXpHAVZC/+mPSMlJygYabpLQbrdh939qh5feoOCgGDGgoqmA/cRoTMkXRi+3ptjPst1Cs6hhyvoz5o+rSBj497wfb/T53t/REHxpAcVBBWX9frELsf3nQoCjZ8rmPP8DQUjRlGG+a4R1a47FIwonq49323WK/i+vEDB39ZdCvqtP1XQT7W/xr0KCnNNKvg7PFIt31nCv5WLwzZfr5YLAGG//7cKRh0fUNDPXR7T3L3D97hXwXeEQ8J2owCaVdYAAAAAAENiBAsAAAAAEkKABQAAAAAJIcACAAAAgIQQYAEAAABAQjotFFsYBx98sC9ZsiTvZgAAUnT99dff6+6Luu9ZTPRVAFBtvfZTpQiwlixZos2bN+fdDABAiszsthzecx9J1ygoebyXpG+4+4fN7AIFZZgfDHc9yd23dnot+ioAqLZe+6lSBFgAAKTk95JWufsj4aLWPzCz5lpB6939Gzm2DQBQQgRYAIDa8mAxyEfCuyPhDwtEAgAGRpELAECtmdlCM9sq6R5JV7n7deFDZ5rZDWZ2jpntHfPcdWa22cw279ixI7M2AwCKiwALAFBr7r7L3ZdLerqkY8zsaEmnSXqOpP8g6SBJH4p57rnuvtLdVy5aVNr6HACABBFgAQAgyd1nJF0t6dXuvt0Dv5f03yUdk2vjAAClQYAFAKgtM1tkZmPh7VFJr5B0i5kdFm4zSWsk/Sy/VgIAyoQiFwCAOjtM0oVmtlDBRcdL3P3bZrbJzBZJMklbJf11no0EAJRHagGWmR0h6SJJT5P0hKRz3f0zZnaGpPdIas4GPt3dr0irHQAAxHH3GyStiNi+KofmAAAqIM0RrMclneruPzGz/SVdb2ZXhY+d4+6fTPG9AQAAACBzqQVY7r5d0vbw9sNmdrOkRlrvBwAAAAB5y2QOlpktUZCCcZ2kcUnvN7N3StqsYJTrgYjnrJO0TpIWL16cRTMBAH2Y2jKts668VXfNzOrwsVGtX32U1qzgOhoAlBHn9OSkXkXQzJ4s6VJJJ7v7Q5I+J+mZkpYrGOH6VNTzWFsEAIprasu0TrvsRk3PzMolTc/M6rTLbtTUlum8mwYA6BPn9GSlGmCZ2YiC4Oor7n6ZJLn73eGijk9I+oJYWwQASuesK2/V7M5dc7bN7tyls668NacWAQAGxTk9WWlWETRJ50m62d3Pbtl+WDg/S5LeINYWAYBC6SVN5K6Z2cjnxm0HABQX5/RkpTkHa1zSOyTdaGZbw22nSzrBzJZLcknbJL03xTYAAPrQTBNpXslspolImhNkHT42qumIjvfwsdFsGgoASAzn9GSlliLo7j9wd3P357v78vDnCnd/h7svC7f/p5bRLABAznpNE1m/+iiNjiycs210ZKHWrz4q9TYCAJLFOT1ZmVQRBACUQ69pIs3RLCpOAUD5cU5PFgEWANRIt/lV/aSJrFnRoPMFgIrgnJ6c1Mu0AwCKoZcyvKSJAAAwHAIsAKiJXuZXrVnR0Ia1y9QYG5VJaoyNasPaZVzVBACgR6QIAkCJ9FJCPU4/86sIqAAAVTBMvzkoAiwAKIleS6jHoQwvAKBOhu03B0WKIACURK8l1OMwvwoAUCfD9puDYgQLAEqi1xS/Vu2pEW98UUPfv2UHZXgBAJU3SL+ZBAIsACiJflP8olIjLr1+mqIVAIBayCs1nhRBACiJflP88kqNAACgCPJKjWcECwBKojnq1Gs1pLgUiKireQAAVE2//WZSCLAAoET6KaEelxphCtIHSRMEAFRdHkuPkCIIABW1fvVRsojtLpEmCABASgiwAKAkprZMa3xyk5ZObNT45CZNbZnuuP+aFQ15zGNpV1ACAKCuCLAAoASaFQGnZ2bl2rNYYrcgqxFTKYnFhQEASAcBFgCUwKAVAVlcGACAbFHkAgAKrLlQcFzlv26pfnlVUAIAoK4IsACgoNoXCo7SS6pfHhWUAACoK1IEAaCgotICW5HqBwBA8TCCBQAF0UwHbKbydVoQuEGqHwAAhUSABQAF0J4OOD0zK5Miy6w3xkZ17cSqTNsHAAB6Q4ogABRAVDqgS/MWCiYtEACAYmMECwCG0J7WN2jaXlw1QFcwYkUFQAAAyoEACwAGFJXWd9plN0pS30FQ3Jwr0gEBACgXUgQBYECDLv4bhQWBAQCoBkawAGBAcWl93Rb/jcKCwAAAVAMBFgAMKC6tr5fFf6MkuSBwUnPDAABAf0gRBIABFTWtrzk3bHpmVq49c8Omtkzn2q4iMrN9zOxHZvZTM7vJzD4Sbl9qZteZ2S/M7GIze1LebQUAlAMBFgAMaM2KhjasXabG2KhMQUGKDWuX5T5SlOTcsBr4vaRV7v4CScslvdrMXiLpv0g6x92PlPSApHfn2EYAQImQIggAQxgkrS/t9L0k54ZVnbu7pEfCuyPhj0taJelt4fYLJZ0h6XNZtw8AUD4EWACQoSRLu8dJem5Y1ZnZQknXS3qWpH+W9CtJM+7+eLjLnZKYwAagUpirmx5SBAEgQ1mk7xV1blhRufsud18u6emSjpH0x1G7RT3XzNaZ2WYz27xjx440mwkAiWGubroIsAAgxtSWaY1PbtLSiY0an9yUSMeTRfpeUeeGFZ27z0i6WtJLJI2ZWTPL4+mS7op5zrnuvtLdVy5atCibhgLAkJirmy5SBAEgQlqpfFml7yVZ8r3KzGyRpJ3uPmNmo5JeoaDAxfcl/bmkr0s6UdK38mslACSLubrpYgQLACKkdXWP9L3COUzS983sBkk/lnSVu39b0ock/Z2Z/VLSUyWdl2MbASBRcRf1mKubDEawACBCt6t7g04Obu7DxOJicPcbJK2I2P5rBfOxAKBy1q8+ak6WhsTFviQRYAFAhE6pfMOmD5K+BwDIExf70kWABQAROl3d65Q+SOcEACgDLvalhwALACJ0urp3ysVbI5/Ty+Rg1h0BAKDaCLAAIEbc1b1BKwFmscgwAADIF1UEAaBPg1YCZN0RAACqjxEsAJWSRQreoJODWXcEAIDqI8ACUBlZpuANMjk4q0WGAQBAfkgRBFAZRU/BY5FhAACqjxEsAJWRRwpePymJrDsCAED1EWABqIysU/AGSUlk3REAAKqNFEEAlZF1Cl7RUxIBAED2GMECUBlZp+BRFRAAALQjwAJQKXEpeGmUb6cqIAAAaEeKIIDKa86Vmp6ZlWvPXKmpLdNDvS5VAQEAQDsCLACVl9ZcqTUrGtqwdpkaY6MySY2xUW1Yu4wiFgAA1BgpggAqr9tcqWHSB6kKCAAAWhFgAai8TnOlBim1DgBAGaQx/xjdkSIIoPI6zZWi1DoAoIrSmn+M7lILsMzsCDP7vpndbGY3mdkHwu0HmdlVZvaL8N8D02oDAEhz50pJ0kKz3UFU1MiWRKl1AEC5cQExP2mOYD0u6VR3/2NJL5H0PjN7rqQJSd9z9yMlfS+8DwCpWrOisXska5e7pOBqnsXsT6l1AECZsVZjflILsNx9u7v/JLz9sKSbJTUkHS/pwnC3CyWtSasNANAq6mqeS/OCLEqtAwDKLu5CIRcQ05fJHCwzWyJphaTrJB3q7tulIAiTdEjMc9aZ2WYz27xjx44smgmg4uKu2rlEqXUAQKWwVmN+Uq8iaGZPlnSppJPd/SGzuIScudz9XEnnStLKlSs9vRYCqIuxfUf0wGM7520/cN8RXTuxKocWAQCQjuaFQqoIZi/VAMvMRhQEV19x98vCzXeb2WHuvt3MDpN0T5ptAIAmj7lUE7cdAIAyY63GfKRZRdAknSfpZnc/u+WhyyWdGN4+UdK30moDALR6cHb+6JUkzczupGwtAABIRJpzsMYlvUPSKjPbGv68VtKkpFea2S8kvTK8DwCp6zSxl7VBAABAEtKsIvgDdzd3f767Lw9/rnD3+9z9OHc/Mvz3/rTaAACtoib8NrE2CAAASELqRS4AIEtTW6ZjJ/Q2/z354q2Rz2VtEABAEXTqy1D845NJmXYAyMLUlmmddtmNmp6ZlStYSLg99W/NioYarA0CACioXvqyOivD8SHAAlAZUQsJR6X+sTYIAKCoeu3L6qoMx4cUQQCVEZfid9fM7Lx0gje+qKHv37KjsOkFAIB66tSXoRzHhwALQGUcPjaq6YgT7Ni+Izrtsht3X/GanpnVpddPa8PaZQRVAIBCievLSGMPlOH4kCIIoDLiUv/cVfh0AgAAJNLYu+l2fKa2TGt8cpOWTmzU+OSmXOZmMYIFoDKao1HtlYVOSalqYNGrGAEAyieuLytj/5JGP9np+DQLYLRmrJx22Y1znpcFAiwAlbJmRWPeSfSsK29NPJ2gKCdxAED1RPVlZZNmPxl3fDoVwMjyeJIiCKDy0ki3KEMVIwAA8pJHP1mUAhgEWAAqb82KhjasXabG2KhMUmNsdOgCF0U5iWM4ZnaEmX3fzG42s5vM7APh9jPMbNrMtoY/r827rQBQJnn0k3GZKVkXwCBFEEDhpJWznWR6QBmqGKEnj0s61d1/Ymb7S7rezK4KHzvH3T+ZY9sAoLTy6CfXrz5qTlqilE+BEEawABRKGVZol6jyVBXuvt3dfxLefljSzZLKPfEBAAogj34yjYyVQTCCBaBQijJBtZsqVXlCwMyWSFoh6TpJ45Leb2bvlLRZwSjXAxHPWSdpnSQtXrw4s7YCqI+yVqzNq58sQoEQc/dcG9CLlStX+ubNm/NuBoAMLJ3YqLizUmNstHQdDHpnZte7+8qc3vvJkv5N0pnufpmZHSrpXkku6WOSDnP3v+z0GvRVAJLWXolPCkaB8hiVQe/9FCmCAAolLjfbpMKnDaKczGxE0qWSvuLul0mSu9/t7rvc/QlJX5B0TJ5tBFBPVKwtJwIsAIUSlbNt0rxRLToYJMHMTNJ5km5297Nbth/WstsbJP0s67YBABVry4kAC0CuprZMa3xyk5ZObNT45CZJmjdBNS5lkA4GCRiX9A5Jq9pKsn/CzG40sxskvVzSKbm2EkAtFaXsOPpDkQsAuYlb5X3D2mW6dmLV7v3GJzdREh2pcPcfKBgkbXdF1m0BgHZFKTuO/jCCBSA3veaWUxIdAFBHRSk7jv4wggUgNd1Ky/aaW05JdABAXRWh7Dj6Q4AFIBVx6X/SnoCpn1Xe6WAAAEAZkCIIIBW9pP+R+gcAAKqGESwAqeg1/W/vvRbsDsQO3HdEH/6z5zFSBQAAetZtSkLWGMECkIpupWWbKYQzszt3P/a7nU9k0jYAAFANze8T0zOzcu2ZkjC1ZTq3NhFgAUhFt/Q/VqcHAADDKuL3CVIEAXQ1yNB7t8p/rE4PAACGVcTvEwRYADrqpRpgnE6V//qpIAgAABCliN8nSBEE0FFaQ+9UEAQAAMMq4vcJRrAAdDTs0HtceiGLBwMAUH55V/Ar4vcJAiwAHQ0z9N4tvZDFgwEAKK9hphEkqWjfJ0gRBNDRMEPvRazsAwAAkkE/H40RLAAdDTP0XsTKPgAAIBn089EYwQKQmm6LDQMAgPKin49GgAWgo2FWSC9iZR8AAJIytWVa45ObtHRio8YnN/XUN1YJ/Xw0AiwAHQ2TX71mRUMb1i5TY2xUJqkxNqoNa5cVaiIqAACDGOYCZFXQz0djDhaAjobNr+5W2Sfv8q4AAAyi0wXIOvVj/VTwq0ufT4AFoKM0V0gvSnlXAAD6RYGH/tSpzydFEEBHaeZXU94VAFBWFHjoT536fAIsAB1F5Ve/8UUNnXXlrUNP6uXqHwCgrCjw0J869fmkCALoqjW/Oskh/jTTDwEASNMw60TWUZ36fAIsAH1JclLv+tVHzQnWJK7+AQAGk0cBhX4KPNRdnfp8AiwAc3TroJIc4ufqHwAgCXUqoFBWderzCbAA7NZLB5X0ED9X/wAAw6JkejnUpc+nyAWA3Xqp8MOkXgBA0dSpgAKKjxEsoCZ6yU3vpYOq0xA/AKAc6lRAAcVHgAXUQK+56b12UHUZ4gcAlEOdCiig+EgRBGqg18X9SP8DAJRR1JqNG9Yu42IgcsEIFlADcal/7aNVpP8BAMqK7AoUBQEWUANxqX+mIH2wtUOigwIAABgcKYJADaxffZQsYrtL89IEAQAAMDgCLKAG1qxoyGMe67WE7dSWaY38/K1sAAAgAElEQVRPbtLSiY0an9ykqS3TyTUQAACgIgiwgJpoxJSq7aWEbbMK4fTMrFx7qhASZAEAAMxFgAXUxDAVAnutQggAAFB3qRW5MLPzJb1e0j3ufnS47QxJ75G0I9ztdHe/Iq02AHXSbSHhYSoE9rIAMQAAyFa3vh/5SLOK4AWSPivporbt57j7J1N8X6B2el1IeNAKgb0uQAyUjZkdoaCfepqkJySd6+6fMbODJF0saYmkbZLe7O4P5NVOAOkpa5DSa9+fR7vKeDyTlFqKoLtfI+n+tF4fwB5pp/CxADEq7HFJp7r7H0t6iaT3mdlzJU1I+p67Hynpe+F9ABVT5jnGRUzfL/PxTFIec7Deb2Y3mNn5ZnZg3E5mts7MNpvZ5h07dsTtBkDpp/CtWdHQhrXL1BgblSkomLFh7bLaXZFC9bj7dnf/SXj7YUk3S2pIOl7SheFuF0pak08LAaSpiEFKr4qYvl/m45mkrBca/pykjylYfudjkj4l6S+jdnT3cyWdK0krV66MqzANVFK/w+tZpPCxADGqzsyWSFoh6TpJh7r7dikIwszskJjnrJO0TpIWL16cTUMBSEomFa2IQUqvipi+n+TxLHOqYaYjWO5+t7vvcvcnJH1B0jFZvj9QBoMMr5PCBwzHzJ4s6VJJJ7v7Q70+z93PdfeV7r5y0aJF6TUQwBxJpaLFBSNlmGOcZt8/6NqXSR3PsqcaZhpgmdlhLXffIOlnWb4/UAaDDK+TwgcMzsxGFARXX3H3y8LNdzf7rPDfe/JqH4D5kkpFK/MFyrT6/mGCm6SOZ9lTDdMs0/41ScdKOtjM7pT0YUnHmtlyBSmC2yS9N633B8pq0OH1pFL4yjwkD/TLzEzSeZJudvezWx66XNKJkibDf7+VQ/MAxEgqFW2YJUyKII30/bjg5tRLfqpTLt7a8RgldTzLnLoppRhgufsJEZvPS+v9gKrIM6e6qCVfgRSNS3qHpBvNbGu47XQFgdUlZvZuSbdLelNO7QMQIcm+kjnGc8UFMbs8KInQ7btBEseziPPL+pFHFUEAHeSZrlD2IXmgX+7+A3c3d3++uy8Pf65w9/vc/Th3PzL8l2VHgAIpc2pf0fUSxKT93aDsv9+sqwgC6CLPdIV+huRJJQSAYqrD+blbX1mHY5CW9auPmpPNEifNdL2yp24SYAEFlFe6Qq9D8qQSAkAx1en8HNdX1ukYpKE9uFlgtjs9sFXa6XplTt0kRRDAbr0OyZNKCADFxPmZY5CENSsaunZilX4z+Tp96s0vKHW6Xh4YwQIKKo/0hl6H5Mte3QcAqorzc3GPQVnTFsuerpcHAiyggPJMb+hlSL7s1X0AoKo4Pyd/DJIIjJLs1/O6AEtA1TtSBIECKnp6Q9mr+wBAVXF+TvYYDLPobquk+vWk2oN0EWABGZvaMq3xyU1aOrFR45ObIk+KRU1vaEpr9XgAwHA4Pyd7DJIKjJLq14t+ARYBUgSBDPWaIlCGFA/SBQCgmDg/J3cMkgqMkurXi34BFgFGsIAM9XrliRQPAADyFxcA9RsYJdWvJ9UepIsAC8hQr1eehk1v6CUNEQAAdJZUYJRU2iIXYMuBFEEgQ/2kCAya3sACiwAAJCPJEuVJpC1SMr0cCLCADK1ffdSc4EdK/spTpzRETsAAAPSnaHPaitYezEeABWSo05WnpNa1YAIsAABAfgiwgIxFXXlKMq2vDBUIAQAAqooiF0ABJLmuBRNgAQAA8sMIFlAASab1MQEWAAAgPwRYQAHEpfW5pPHJTX0HSEyABQBgj6TmOQO9IEUQKICotL6m5nws1rICABRJWdZcbM5znp6ZlYt+FemLDbDM7AozW5JdU4D6al2AMMqg87GAqqOvAvJRpqAlyXnOyEdZgvmmTiNYF0j6rpn9ZzMbyag9QG2tWdHQtROrZDGP9zIfq2wnICABF4i+CshcmYIWli8ptzIF802xc7Dc/RIz2yjpHyVtNrMvSXqi5fGzM2gfUDuDlllPstQ7UBb0VUA+yhS0sHxJuXUK5ov6/abbHKydkh6VtLek/dt+AKRg0DLrZbqaCCSMvgrIWFxwUsSgheVLyq1MwXxT7AiWmb1a0tmSLpf0Qnd/LLNWATXRqapRv9WOyngCAoZFXwXkY/3qo+ZkTUjFDVpYvqTcyjgC2alM+3+W9CZ3vymrxgB10i2lr98TfxlPQEAC6KuAHJQtaGnvV5tzlsvQ9rorUzDf1GkO1kuzbAhQN0nnFJfxBAQMi74KyE8aay5msV4Vc5bLpWzBvMRCw0AmojqMpFP6yngCAgCgKavAp4xFE+oujWA+TQRYQMriOoyxfUf0wGM75+0/TEpf2U5AAAA0xQU+p17yU51y8dbELhwyZxlpI8ACUhbXYey91wKNjiwkpQ8AUDmDpPrFBTi73CUlN6LFnGWkrVuZdgBDiuswZmZ3au+9FujAfUdkkhpjo9qwdhkjUACAUuu2MGyzwMTSiY0an9y0e3svAU4Sy49Qth1pYwQLSFnclTIpCLJGRxbqnLcsJ7ACAFRCt3UZ4+ZZRRVrijJsKh9zlospiwInWSHAAlLWrcNgYi0AoEo6zXHqFHxdO7FK0p7AZ4HZ7vTAVkmk8jFnuViqVtmRAAu1ldWVktYrZXEjWUysBQBURac5TnH93fTMrJZObJzTH7d/6ZZI5auqqlV2ZA4WaqlbfnjS1qxo6NqJVWrEXHVjYi0AoCo6zXHq1N+198drVjS0Ye0yNcZGmatccVWr7MgIFmopryslLAYMAKi6bnOcus2zau2PSeWrh6pVdiTAQu1MbZnOLVWPibUAgDqIC4za+8H5M6wCZR25wGCqdgGaAAu10kwNjJPFlRKuxgEA6qy1Hxyf3FSpkQsMpmoXoAmwUCtRqYFNZb5SAmAwZna+pNdLusfdjw63nSHpPZJ2hLud7u5X5NNCoNqqNnLRqkplx7NQpQvQBFiolU4pB3vvtUCnXLxVZ115KydBoD4ukPRZSRe1bT/H3T+ZfXOA4ugnQBg0mKjayEVT1cqOoz8EWKiVuEmUpmDRX4mTIFAn7n6NmS3Jux1A0fQTIAwbTFRp5KKpamXH0R/KtKNWokrHmjRvkm3rivMAaun9ZnaDmZ1vZgfG7WRm68xss5lt3rFjR9xuQOl0ChCG2bcuqlZ2HP0hwEKtRK2pQQUjAG0+J+mZkpZL2i7pU3E7uvu57r7S3VcuWrQoq/YBqesnQCCYmC+uSAfFO+qBAAu1d+C+I5HbOQkC9eTud7v7Lnd/QtIXJB2Td5uArPUTIBBMzNdpsWVUHwEWaqWZJz4drr0xPTOrR373uEYW2pz9OAkC9WVmh7XcfYOkn+XVFiAvUQHCyALTY394XEsnNmp8cpOmtkzH7lv3fjQqY2bD2mXMv6oJilygVqLyxHc+4RobHdF+e+9VqQpGALozs69JOlbSwWZ2p6QPSzrWzJYrmJ65TdJ7c2sgkLHWaoAHjI5on5EFmnlspw4YHdGjf3hcDzwWXxCqapUAh1XF4h3oDQEWaiUuH/zB2Z3a+uFXZdwaAHlz9xMiNp+XeUOAAmivBjgzu1OjIwt1zluW66wrb91dbbeptSoewQSwBymCqJWxmPlWcdsBAKiLTtUAKWQB9I4AC7XiMSUD47YDAFAXnYIoClkAvSNFELXyYFt6Q7ft/Rp0JXsAAPJ2+NiopiOCrGZ/1po+KFHIoh3fAdDECBZqJc0rcFEVCk+77MbdVZYAACiyTtUAqYrXGd8B0IoRLNRKmlfgOuWu0wEBAIquWzVAClnE4zsAWhFgoVaSLCXbngoQlVYhMQEYAFAeBFGD6bcICOmE1UaAhdpJovNoL2U7PTMrU7BoTjsmAAMAUG2d5q+1i/oO0b6mGMqNOVjAAKJSAVySte3HBGAAAKqv0/y1dp3SCVENqY1gmdn5kl4v6R53PzrcdpCkiyUtkbRN0pvd/YG02gAkIWoYP27I3xVM/GXIHwCA+uhnCgJrilVfmimCF0j6rKSLWrZNSPqeu0+a2UR4/0MptgEYStww/ti+I3rgsfml3Rtjo7p2YlXWzQQAADnrdQpCP+mEKKfUUgTd/RpJ97dtPl7SheHtCyWtSev9gSTEDeO7q+dUAAAAgKZ+0glRTlkXuTjU3bdLkrtvN7ND4nY0s3WS1knS4sWLM2oe6iqumk/ccP2Dszt1zluWUwEIAAD0JcmKxu2oTlgMha0i6O7nSjpXklauXBlVnA1IRKdqPp2G8SllCwAABpHGdwiqExZH1lUE7zazwyQp/PeejN8fmKdTNR+G8QEAZTC1ZVrjk5u0dGKjxic3aWrLdN5NQsaoTlgcWY9gXS7pREmT4b/fyvj9gXni0gCnZ2ZTHcYHACAJjFxA6l6dkPTB7KRZpv1rko6VdLCZ3SnpwwoCq0vM7N2Sbpf0prTeH+hVXBqgKTgZkQoIACiyTiMX9F/10WlaA0F4ttKsIniCux/m7iPu/nR3P8/d73P349z9yPDf9iqDQObWrz5q3gLBUrCmFcPqAIAiak0JjPpSLbGuUt10mtZA+mC2sp6DBRTOmhUNxVVRoXMCABRNczRiemY2tv+SWFepbtasaGjD2mVqjI3KFKzNuWHtso5Vkfmek47CVhEEktQt77jBon8AgJKIGo1oR0Gmeoqb1sDixtliBAuV136lr5l33FphiWqBAICy6DTq0D5yAUh8z8kaI1iovF4m/1ItEABQFnGjEY2xUV07sSqHFqHo+J6TLQIsVF6nMuzNKoFSOov+AQCQtPWrj5pTEU5iNALd8T0nO6QIovI65Re3pwoCAFB0nYoZAMgfI1iovKgrfU2sEwIAyNOgi78yGgEUFwEWKqu10zpgdCS24hIlSgEAeWDxV6CaCLBQSe2d1szsTpkUuV4IJUoBAHnopQhTVQw6UpfW6wBpIsBCJUV1Wi7NC7KYFAwAyEtdFn9NaqSuyiN+BI7VQpELVFJc5+SSDtx3ZPf9vffivwAAIB9xGRRR26e2TGt8cpOWTmzU+OSmUhVo6jRSl8frFE0v63WiXBjBQiXFrRFy4L4j+t3OJ3bfn5ndWZmrXwCAculWbr05qjE9MzsnA6NsIzdJjdRVdcSvTqmidcHle1RS3Irl7qrk1S8AQPl0KrfeOqohzZ9DXKa+q5+Ruixep2iqGjjWGSNYyFVaOcdxK5afcvHWyP05iQEA8hBXbj1qVKNdWfqupBZGruoCy3FZN2UPHOuMAAu5SXuyalSn1Uy1aMdJDABQJL0ET2Xpu+Iuevbb1yf1OkVT1cCxzgiwkJs8co45iQEAyiBuVKOpbH1XUgsjV3GB5aoGjnVGgIXcpJFz3C3lkJMYAKAMoi4INgtdNOi7KqeKgWOdEWAhN0nnHPeacshJDABQdFwQBMqLAAu5STpdjzKnAPplZudLer2ke9z96HDbQZIulrRE0jZJb3b3B/JqI+qLC4L5YNFfDIsAC5nodLJK6iRGmVMAA7hA0mclXdSybULS99x90swmwvsfyqFtADKWdgEu1AMBFlLX7WSV1AmLMqcA+uXu15jZkrbNx0s6Nrx9oaSrRYAF1ALZMEgCCw0jdZ1OVkmKW1y4TFWWABTCoe6+XZLCfw/JuT2okKkt0xqf3KSlExs1PrlJU1ume3oM2SAbBklgBAupy+Jk1UxBnN25SwvNtMudKksAUmdm6yStk6TFixfn3BoUUWuK/AGjI3r0D49r5y6XNDejQxKpaQVANgySwAgWUhd3UkrqZNVMQWyeEHe57x65olMCMIC7zewwSQr/vSduR3c/191XuvvKRYsWZdZAlENr/+SSZmZ37g6umpoZHVlle6AzsmGQBAIspC7tkxWdEoCEXS7pxPD2iZK+lWNbUGJR/VOUu2ZmSU0riDUrGtqwdpkaY6MyBWuObVi7jAu26Aspgkhd2mt50CkBGJSZfU1BQYuDzexOSR+WNCnpEjN7t6TbJb0pvxYiL0mU6u61H2pmdJCaVgyUx8ewCLCQqLgOKc2TFfnSAAbl7ifEPHRcpg1BoSRVqjuuf2rVmtGR5NqQAPJDiiAS055r3uyQ0q6CRL40ACBJSaWeR/VPIwtMB+47Mi/9jNQ0oDoYwUJi8lo7Iu0URABAvQybet5eOXCfkQWaeWxn1/6J1DSgGgiwMLRmRxKXBpHFXCg6JQBAUvpNPe9Uin1mdqdGRxbqnLcsL2Q/lcRcMwBzkSKIobSXSI/CXCgAQJn0k3reTyn2oskrtR+oOgIsDKVbCVrmQgEAyqaf+VD9lGIvGpY5AdJBiiD61ppO4B32a5BqAAAoqV5Tz/stxZ6HuDRAljkB0kGAhb60l66N0xgb1bUTqzJqFQAA3aUx36jfUuxZ61RynmVOgHSQIoi+9JIKQVogAKBo0ppv1E8p9jx0SgNkmRMgHYxgoS+d0gZM6npFkGpFAIA89LKUyCB9VNGXCumUBlj0tgNlRYCFvsSlE/SSEtgpTYGTOQAgTd3mGw3TRxV5qZBuaYBFbjtQVqQIoi/DpBNQrQgAkJe4eUXN7VXto0gDBLLHCBb6Mkw6QdzVw+mZWY1PbiI9AQDQt17T+tavPmpekabWQKOqFfVIAwSyR4CFvg2aThCXpmDS7u2kDQIAetVPWl+3QKPKFfVIAwSyRYCFzERdPTRp3lpa7ZOOAQCI0kvhiladAo1uI1wUaQLQKwIsdJRkhxJ19TBu7ZCyp2QAANKXZFpfpxEuijQB6AcBFmKl0aG0Xz0cn9xU2ZQMAEC64i7ULTDT0omNfV8YjBvh6nekDEC9UUUQsbKoqER1IwDAoKL6EEna5Z7oYsLdijQN+/oAqoURLMTqJfVi2BRCqhsBAAbV3ocsMNMunzuzN4mRpk4p7aQLAmhHgIVY3SoqJZVCSHUjAMCgWvuQpRMbI/cZdl5vVAGMVqQLAmhFiiBidUvfq+qijACAcuq2mPCg1qxoaMPaZWp0eB2KMwFoIsBCrNYOxSQ1xka1Ye2y3VfoqrooIwCgnNKc17tmRUPXTqyKDbIozgSgiRRB7BY3nyou5aHKizICAMoni3m93dbLAgACLEgabD4VnQwAoGjSntdLcSYA3RBgQdJga3zQyQAA6ojiTAA6IcCCprZMx5af7Tafik4GAJC2YZcEAYAsEWDVXDM1MA7zqQAAeUpqSRAAyApVBGsuKjWwiflUAIC8sSQIgLLJZQTLzLZJeljSLkmPu/vKPNpRFcOkTnRKAWwtyQ4AQJri+jKWBAFQNnmmCL7c3e/N8f0rYdjUibhS642xUYIrAEAmOvVlLAkCoGxIESy5YVMn0lyUEQCAXsT1Zade8lNNz8zK2vannwJQZHkFWC7pu2Z2vZmti9rBzNaZ2WYz27xjx46Mm1cew6ZOrFnR0Btf1NBCC7qvhWZ644uoDAgAyE5cn7XLXVLwpaEZZDXGRklhB1BoeaUIjrv7XWZ2iKSrzOwWd7+mdQd3P1fSuZK0cuVKz6ORZTBs6sTUlmldev307k5sl7suvX5aK59xEJ0XACATcX1ZK1cQXF07sSqbRgERWDIAvchlBMvd7wr/vUfSNyUdk0c7qmDYFD+qMwEAsjK1ZVrjk5u0dGKjxic3aWrLtKToviwKhS2Qp+ZcwemZWbn2zBVs/h0DTZmPYJnZfpIWuPvD4e1XSfpo1u2oiuZVk4/860164LGdkqS99+o9bqY6EwAgC70UZWqODCww251Z0SrpwhaMRqAfnS5K83eDVnmkCB4q6ZsWzPnZS9JX3f07ObSjUn6384ndt2dmd/ZcSZDqTACALHT7ctr8keYHY1LyhS1YwBj94qI0epV5iqC7/9rdXxD+PM/dz8y6DVUzTJofVQQBAFno58vpmhUNbVi7TI2xUZnmF7aISzWMErcvKfLoV9zFZy5Ko12e62AhIXGd1vTMrKa2THe8EteelkGKBAAEzGybpIcl7ZL0uLuvzLdF5dZvxkTriFarfkaeOu3LaAT6tX71UamPrKIaCLAqoFP1pV7SHeI6MQCAXu7u9+bdiCpI6stpP/NgOu1Lijz6xUVp9IoAqwKiOq0mJl8CAIogqS+n/Yw8ddr3nLcsZzQCfeOiNHpBgFUBzf/oJ1+8NfLxJNIdqLQEoIZc0nfNzCV9PlyfcQ4zWydpnSQtXrw44+aVTxJfTvsZeeq0L6MRANJCgFURa1Y0dNaVt6aS7kClJQA1Ne7ud5nZIZKuMrNb3P2a1h3CoOtcSVq5cuX8uuJIXD+pht32ZTQCQBpyWWgY6UirIiCVlgDUkbvfFf57j6RvSjom3xYVU6eKfv1U++tVtwqDg+4LAElhBKvEotL2Nqxdlni6A5WWANSNme0naYG7PxzefpWkj+bcrMLplOEgqWP2wzCp5/2MPDFKBRRXVaegEGCVVFyntmHtMl07sSrR96LSEoAaOlTSN81MCvrKr7r7d/JtUvF0y3Do9Bip50C9VXkKCimCJZVl2h6LEQOoG3f/tbu/IPx5nrufmXebiqhThkOnx0g9B1Dl8wAjWCWVZdoelZYAAE2tKT0LzLTL59f2cEkLYx47fGyU1HMAlT4PEGAVWKe81KzT9shhBwC0p/REBVBNUY81sx/SqnoLoDyqPAWFFMGCanZi0zOzcu3JS21WYCJtDwCQlrjqf1EpPVIwWhVnodm8Cn70YQCqfB5gBKugOuWlto4mkbYHAEhSp4nncak7T7jLFKQGRj32m8nXzdlGHwagyucBAqyC6paXWtWylgCAdPTab3S6wNctpaefdB9SzwFU9TxAgFVQnTqxKpe1BAAkr59+I+4CX7NPah+pak3paX2P9sdQHFykBdLFHKyC6pSXWuWylgCA5PXTb3SbYO4Kgixp7ryqNSsa2rB2mRpjo/PmXKE4us3xBjA8RrAKqlNe6ikXb418zvTMrKa2TNOZAQDm6Kcc8vrVR80biWrnCgKo9oXtq5ruUyXd5ngDGB4BVoHFdVRx6YOSSBUEAMzTTznk9gt8cYXYq7BWTR1Vee0hZIMU0+5IESyhqPTBJlIFAQDt+i2HvGZFQ9dOrNJvJl+nRkzKYBXWqqmjuN8bv0/0ghTT3hBgldCaFQ298UXxVwq4CgUAaDXM/Kgqr1VTR/w+MQzqAPSGFMESmtoyrUuvj79SwFUoAEC7TvOjOqX8VHmtmjri94lhkGLaGwKsEoq6etDEVSgAQC+aQdX0zOyc0utRJdwpXlEt/D4xqH7mc9YZKYI9mNoyrfHJTVo6sVHjk5tyzzPtdJWAkrgAgG5a51FImlfIgpQfAFFIMe0NI1hdFHFR37irB42xUYIrAEBXnTIhmkj5AdCOFNPeEGB1UcT1IqLWKOHqAQCg1/LJvQRPpPwAiEKKaXcEWF10m8yXx1oAXD0AALTrJ+Oi03qKEhftAGAYBFhddJrMl2f6IFcPAKAeer2Q10/GRVQmRLPQRYOLdgAwFAKsLjql4xUxfRAAUB39XMjrp3wymRAAkB4CrC46dUKnXLw18jm9TgzOI70QAFAe3S7ktfYjC8y0y9vrAQajUuOTm+b1MWRCAEA6CLB6ENcJDbMWQBGrEwIAiqXTqFR7PxIVXDXRxwBAdlgHawjDrAXQ6aokAABS/AW7w8dGY0utLzSLfA59DABkgwBrCGtWNLRh7TI1xkZlCiYG97rQbz+58gCAeup0IS+uv3jCXdEhFn0MAGSBFMEhRaUP9jK3apj0QgBAtcT1G1HzgF/+nEU668pbFZcQ2OxH6GMAIB8EWAnrdW4ViwUDAKTu/UZroNW+b7vWfoQ+BgDyQYpgwnqdWzVMeiEAoDr6mZMbN+9KmtuP0McAQH4YwUpYXH779MzsvDK5lMgFAPQzJzduX5N07cSqOdvoYwAgH4xgJaxTfnsz7WNqy3SGLQIAFFmnSoHD7AsAyAcBVsKiKj61okwuAKBVP0t+DLM8CAAgG6QI9qlbhcDWik9RFZwkyuQCAPaIqhQYVX22330BAPkgwOpDrxUCm3nv45ObKJMLAOiqn/lSzK0CgGIjRbAP/VR6kkjlAAAAAOqm8iNYvSz626t+Kj1JpHIAAPqXZL8FAMhepQOsXlP6enX42GjfKX+kcgAAepV0vwUAyF6lUwT7TenrhpQ/AECaku63AADZq/QIVr8pfd2Q8gcASFPS/RYAIHuVDrAGSenrhpQ/AKgHM3u1pM9IWijpi+4+mfZ7ptFvAQCyVekUQVL6AACDMLOFkv5Z0mskPVfSCWb23LTfl34LAMqv0iNYpPQBAAZ0jKRfuvuvJcnMvi7peEk/T/NN6bcAoPwqHWBJpPQBAAbSkHRHy/07Jb24fSczWydpnSQtXrw4kTem3wKAcqt0iiAAAAOyiG0+b4P7ue6+0t1XLlq0KINmAQCKjgALAID57pR0RMv9p0u6K6e2AABKhAALAID5fizpSDNbamZPkvRWSZfn3CYAQAlUfg4WAAD9cvfHzez9kq5UUKb9fHe/KedmAQBKIJcRLDN7tZndama/NLOJPNoAAEAn7n6Fuz/b3Z/p7mfm3R4AQDlkHmDltbYIAAAAAKQtjxGs3WuLuPsfJDXXFgEAAACAUssjwIpaW2Tegh9mts7MNpvZ5h07dmTWOAAAAAAYVB4BFmuLAAAAAKikPAIs1hYBAAAAUEnmPm/wKN03NNtL0v+WdJykaQVrjbytU/lbM9sh6bYMmnewpHszeJ+i4vPz+ev8+SWOQd6f/xnuXtqUhZa+Ku/jWAYco844Pt1xjDrj+HQ3yDHqqZ/KfB2sQdYWyarDNbPN7r4yi/cqIj4/n7/On1/iGNT98w+r2VdxHLvjGHXG8emOY9QZx6e7NI9RLgsNu/sVkq7I470BAAAAIC25LDQMAAAAAFVEgDXXuXk3IGd8/nqr++eXOAZ1//xJ4Th2xzHqjOPTHceoM45Pd6kdo8yLXAAAAABAVTGCBQAAAAAJIcACAAAAgIQQYEkys1eb2a1m9kszm8i7PXkws4Yx8ToAAAUqSURBVG1mdqOZbTWzzXm3J21mdr6Z3WNmP2vZdpCZXWVmvwj/PTDPNqYp5vOfYWbT4d/AVjN7bZ5tTJOZHWFm3zezm83sJjP7QLi9Fn8DHT5/bf4G0kJ/0lnd+ppe1L0/6qbu/VUv6t6ndZNHn1f7OVhmtlDBwsevlHSngoWPT3D3n+fasIyZ2TZJK929FovSmdnLJD0i6SJ3Pzrc9glJ97v7ZPjF6EB3/1Ce7UxLzOc/Q9Ij7v7JPNuWBTM7TNJh7v4TM9tf0vWS1kg6STX4G+jw+d+smvwNpIH+pLu69TW9qHt/1E3d+6te1L1P6yaPPo8RLOkYSb9091+7+x8kfV3S8Tm3CSlz92sk3d+2+XhJF4a3L1Twn6+SYj5/bbj7dnf/SXj7YUk3S2qoJn8DHT4/hkN/gr7VvT/qpu79VS/q3qd1k0efR4AVHOA7Wu7fqXp+0XBJ3zWz681sXd6Nycmh7r5dCv4zSjok5/bk4f1mdkOYklGLVAIzWyJphaTrVMO/gbbPL9XwbyBB9Cfd0df0pnbnogFwropQ9z6tm6z6PAIsySK21TFvctzdXyjpNZLeFw7Jo14+J+mZkpZL2i7pU/k2J31m9mRJl0o62d0fyrs9WYv4/LX7G0gY/Ul39DVIAueqCHXv07rJss8jwAquMB7Rcv/pku7KqS25cfe7wn/vkfRNBakudXN3mKfbzNe9J+f2ZMrd73b3Xe7+hKQvqOJ/A2Y2ouBE+xV3vyzcXJu/gajPX7e/gRTQn3RBX9Oz2pyLBsG5ar6692ndZN3nEWAFk5CPNLOlZvYkSW+VdHnObcqUme0XTvqTme0n6VWSftb5WZV0uaQTw9snSvpWjm3JXPMkHHqDKvw3YGYm6TxJN7v72S0P1eJvIO7z1+lvICW17086oa/pSy3ORYPiXDVX3fu0bvLo82pfRVCSwrKMn5a0UNL57n5mzk3KlJn9kYIriZK0l6SvVv0YmNnXJB0r6WBJd0v6sKQpSZdIWizpdklvcvdKTqyN+fzHKhgmd0nbJL23mbtdNWb2J5L+p6QbJT0Rbj5dQU525f8GOnz+E1STv4G01L0/6aSOfU0v6t4fdVP3/qoXde/TusmjzyPAAgAAAICEkCIIAAAAAAkhwAIAAACAhBBgAQAAAEBCCLAAAAAAICEEWAAAAACQEAIsIEdmdoSZ/cbMDgrvHxjef4aZfcfMZszs23m3EwBQTx36qT81sx+a2U1mdoOZvSXvtgJFQZl2IGdm9veSnuXu68zs85K2ufsGMztO0r4K1mV4fb6tBADUVVQ/JelSSe7uvzCzwyVdL+mP3X0mx6YChUCABeTMzEYUdEznS3qPpBXu/ofwsWMlfZAACwCQl079VMs+P5X05+7+ixyaCBTKXnk3AKg7d99pZuslfUfSq9o7LQAA8tStnzKzYyQ9SdKv8mgfUDTMwQKK4TWStks6Ou+GAAAQIbKfMrPDJH1J0rvc/Yk8GgYUDQEWkDMzWy7plZJeIumUsLMCAKAQ4vopM3uKpI2S/sHd/z3HJgKFQoAF5MjMTNLnJJ3s7rdLOkvSJ/NtFQAAgbh+ysyeJOmbki5y93/Js41A0RBgAfl6j6Tb3f2q8P5/lfScsPzt/5T0L5KOM7M7zWx1bq0EANRVZD8l6TRJL5N0kpltDX+W59VIoEioIggAAAAACWEECwAAAAASQoAFAAAAAAkhwAIAAACAhBBgAQAAAEBCCLAAAAAAICEEWAAAAACQEAIsAAAAAEjI/wFkspw5FHtU1QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c1f411470>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, (ax1,ax2) = plt.subplots(1,2 , figsize = (12,5.5) )\n",
    "\n",
    "ax1.plot(x1, y, 'o')\n",
    "ax1.set_xlabel('X1')\n",
    "ax1.set_ylabel('Y')\n",
    "ax1.set_title('Contant variance of residuals')\n",
    "\n",
    "ax2.plot(x2, y2, 'o')\n",
    "ax2.set_xlabel('X2')\n",
    "ax2.set_ylabel('Y')\n",
    "ax2.set_title('Non contant variance of residuals')\n",
    "\n",
    "fig.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 157,
   "metadata": {},
   "outputs": [],
   "source": [
    "lr = LinearRegression()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 158,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=False)"
      ]
     },
     "execution_count": 158,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lr.fit(x1.reshape(-1,1),y.reshape(-1,1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 159,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=1, normalize=False)"
      ]
     },
     "execution_count": 159,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lr2 = LinearRegression()\n",
    "lr2.fit(x2.reshape(-1,1),y.reshape(-1,1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 161,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c2052e860>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, (ax1,ax2) = plt.subplots(1,2 , figsize = (12,5.5) )\n",
    "\n",
    "ax1.plot(x1, y, 'o')\n",
    "ax1.set_xlabel('X1')\n",
    "ax1.set_ylabel('Y')\n",
    "ax1.set_title('Contant variance of residuals')\n",
    "ax1.plot(x1, lr.predict(x1.reshape(-1,1)))\n",
    "\n",
    "ax2.plot(x2, y2, 'o')\n",
    "ax2.set_xlabel('X2')\n",
    "ax2.set_ylabel('Y')\n",
    "ax2.set_title('Non contant variance of residuals')\n",
    "ax2.plot(x2, lr2.predict(x2.reshape(-1,1)))\n",
    "\n",
    "fig.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Quantile regression**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 162,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = pd.DataFrame(data={'X': x2, 'Y':y2})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 163,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "      q         a         b        lb        ub\n",
      "0  0.05  0.967168  0.271724  0.015685  0.527763\n",
      "1  0.95  0.047464  1.390176  1.261590  1.518762\n",
      "{'a': 0.7524544883050738, 'b': 0.921874887618274, 'lb': 0.7870105641334761, 'ub': 1.0567392111030718}\n"
     ]
    }
   ],
   "source": [
    "mod = smf.quantreg('Y ~ X', data)\n",
    "res = mod.fit(q=.5)\n",
    "\n",
    "quantiles  = np.array((0.05, 0.95))\n",
    "def fit_model(q):\n",
    "    res = mod.fit(q=q)\n",
    "    return [q, res.params['Intercept'], res.params['X']] + \\\n",
    "            res.conf_int().loc['X'].tolist()\n",
    "    \n",
    "models = [fit_model(x) for x in quantiles]\n",
    "models = pd.DataFrame(models, columns=['q', 'a', 'b','lb','ub'])\n",
    "\n",
    "ols = smf.ols('Y ~ X', data).fit()\n",
    "ols_ci = ols.conf_int().loc['X'].tolist()\n",
    "ols = dict(a = ols.params['Intercept'],\n",
    "           b = ols.params['X'],\n",
    "           lb = ols_ci[0],\n",
    "           ub = ols_ci[1])\n",
    "\n",
    "print(models)\n",
    "print(ols)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 165,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1c1d89e4e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xn = np.arange(data.X.min(), data.X.max(), 2)\n",
    "get_y = lambda a, b: a + b * xn\n",
    "\n",
    "fig, ax = plt.subplots(figsize=(8, 6))\n",
    "\n",
    "for i in range(models.shape[0]):\n",
    "    yn = get_y(models.a[i], models.b[i])\n",
    "    ax.plot(xn, yn, linestyle='dotted', color='grey')\n",
    "\n",
    "yn = get_y(ols['a'], ols['b'])\n",
    "\n",
    "ax.plot(xn, yn, color='red', label='OLS')\n",
    "\n",
    "ax.scatter(data.X, data.Y, alpha=.2)\n",
    "legend = ax.legend()\n",
    "ax.set_xlabel('X', fontsize=16)\n",
    "ax.set_ylabel('Y', fontsize=16)\n",
    "ax.set_title('Quantile regression with 0.05 and 0.95 quantiles')\n",
    "\n",
    "fig.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### End"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.4"
  },
  "toc": {
   "nav_menu": {},
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": false,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
   "toc_cell": false,
   "toc_position": {},
   "toc_section_display": true,
   "toc_window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
